Kelly Criterion Calculator
Find the Kelly criterion fraction from your win rate and win/loss ratio: the optimal share of capital to stake, plus the safer half-Kelly.
Enter how often the trade wins and how big an average win is versus an average loss. You get the fraction of capital that maximizes long-run growth — and the gentler half-Kelly most traders actually use.填入交易的胜率，以及平均盈利相对平均亏损的倍数。即可得到——能让长期复合增长最大化的下注比例，以及多数交易者实际采用的、更温和的「半凯利」。
Fill in both fields to size the bet.填入两个字段即可计算下注比例。
- Half-Kelly半凯利
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- Implied edge隐含优势
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- Loss probability败率
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The Kelly fraction is the share of capital to stake so that long-run compound growth is fastest. It rises with your win rate and with the size of a win relative to a loss, and it turns negative — telling you not to bet at all — the moment those two together stop paying. It answers one question only: given a known edge, how much is too much?凯利比例是——为使长期复合增长最快——应投入的资金份额。它随你的胜率以及盈利相对亏损的倍数而上升；一旦这两者合起来不再带来正收益，它就转为负值——告诉你根本不该下注。它只回答一个问题：在优势已知的前提下，下多少才算过头？
01The formula公式
where W = win probability (as a decimal), R = win/loss ratio其中 W = 胜率（小数形式），R = 盈亏比
Kelly % = 100 × f凯利 % = 100 × f
Half-Kelly % = Kelly % ÷ 2半凯利 % = 凯利 % ÷ 2
R is the ratio of your average win to your average loss, in R-multiples — win $200 on a typical winner and lose $100 on a typical loser, and R = 2. If f comes out at zero or below, the edge does not clear its own losses: Kelly says stand aside, not bet small.R 是你的平均盈利与平均亏损之比，以 R 倍数计——典型盈利赚 $200、典型亏损亏 $100，则 R = 2。若 f 算出为零或更低，说明优势填不平自身的亏损：此时凯利的结论是空仓，而非小注。
02A worked example一个算例
Suppose a trader wins 55% of the time, and a typical win is twice the size of a typical loss (R = 2).假设一位交易者的胜率为 55%，且典型盈利是典型亏损的 两倍（R = 2）。
- W = 0.55, R = 2W = 0.55，R = 2
- f = 0.55 − (1 − 0.55) ÷ 2 = 0.55 − 0.225 = 0.325f = 0.55 − (1 − 0.55) ÷ 2 = 0.55 − 0.225 = 0.325
- Kelly = 32.5% of capital凯利 = 资金的 32.5%
- Half-Kelly = 16.25% — the size most traders actually run.半凯利 = 16.25%——多数交易者实际采用的仓位。
Full Kelly here says stake nearly a third of the account on one bet. That is mathematically growth-optimal only if the 55% and the 2× are exactly right and never change — which is a heroic assumption. That gap between the clean math and the messy edge is why half-Kelly exists.此处的完整凯利建议在一笔下注上押上账户近三分之一。这在数学上是增长最优的——但仅当那 55% 与 2× 分毫不差且永不改变时才成立，而这是一个近乎苛刻的假设。正是这道「干净的数学」与「模糊的真实优势」之间的裂缝，催生了半凯利。
03The common trap常见陷阱
Full Kelly is brutally volatile — even when the inputs are correct, drawdowns of 50% or more are ordinary along the way. Worse, traders rarely know their true win rate; an overestimate pushes f too high, and betting above Kelly lowers growth and raises risk at the same time — the worst of both. This is why the common practice is half-Kelly (or less): it keeps most of the growth for a fraction of the swings, and it forgives an over-optimistic estimate.完整凯利波动极其剧烈——即便输入无误，途中出现 50% 甚至更大的回撤也属寻常。更糟的是，交易者很少知道自己真实的胜率；高估会把 f 推得过高，而下注超过凯利会同时——降低增长并抬升风险，两头皆输。这正是普遍采用半凯利（或更低）的原因：以一小部分的波动换取大部分的增长，并为过于乐观的估计留出余地。
04Where this breaks它的局限
Kelly assumes a known, stable, repeatable edge and independent bets. Trading offers almost none of those cleanly. A few honest limits:凯利假设优势是已知、稳定、可重复的，且各次下注相互独立。而交易几乎无一能干净地满足。几点诚实的局限：
- The edge is estimated, not known. W and R come from a finite, noisy sample of past trades. A small sample can flatter you; Kelly then sizes off a number that may not survive the next hundred trades.优势是估计的，而非已知的。W 和 R 来自过往交易这一有限且带噪声的样本。小样本容易让人自我美化；凯利于是按一个未必能挺过下一百笔交易的数字来定仓。
- Edges drift. A win rate is not a constant of nature — regimes change, crowding erodes an edge, and a strategy that paid last year may not this year. Kelly has no memory of that decay.优势会漂移。胜率并非自然常数——市场环境会变、拥挤会侵蚀优势，去年有效的策略今年未必有效。凯利对这种衰减毫无记忆。
- Correlated bets. Kelly sizes one independent bet. Run several correlated positions at their individual Kelly sizes and your true stake — and true risk — is far larger than any one number suggests.相关的下注。凯利为单一的独立下注定仓。若你按各自的凯利仓位同时持有多个相关头寸，你真实的敞口——与真实的风险——将远大于任一单独数字所暗示的。
Kelly tells you the most you could bet if your edge were certain. Because it never is, sizing below it — half-Kelly or less — is the honest default.凯利告诉你——若优势确定无疑——最多能下多少。而正因优势从不确定，把仓位定在它之下——半凯利或更低——才是诚实的默认选择。
Ground it in the lesson on 在这节课中打好基础 position sizing仓位管理, or turn a win rate and payoff into an edge with the ，或用 risk-to-reward calculator盈亏比计算器.把胜率与赔付换算成优势。